Question

What is an equation of the line that is perpendicular to y=−4/5x+3 and passes through the point (4, 12) ?

Answer 1

Let $k:y=m_1x+b_1$ and $l:y=m_2x+b_2$

$l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have

$y=-\dfrac{4}{5}x+3\to m_1=-\dfrac{4}{5}$

Therefore

$m_2=-\dfrac{1}{-\frac{4}{5}}=\dfrac{5}{4}$

We have the equation of a line:

$y=\dfrac{5}{4}x+b$

Put the coordinates of the point (4, 12) to the equation of the line:

$12=\dfrac{5}{4}(4)+b$

$12=5+b$        subtract 5 from both sides

$7=b\to b=7$

Answer: $\boxed{y=\dfrac{5}{4}x+7}$